Use separation of variables to solve uxx+2uy+uyy=0, u(x, 0) = f(x), u(x, 1) = 0, u(0,...

Use separation of variables to solve uxx+2uy+uyy=0, u(x, 0) = f(x), u(x, 1) = 0, u(0, y) = 0, u(1, y) = 0.

Expert Solution

Colby Messinger answered 1 year ago

Please solve the following: ut=uxx, 0<x<1, t>0 u(0,t)=0, u(1,t)=A, t>0 u(x,0)=cosx, 0<x<1

1. Solve by separation of variables yy'= xy2 + x, y(1)=0 a. Solve by the integrating...

1. Solve by separation of variables yy'= xy2 + x, y(1)=0 a. Solve by the integrating factor method xy'+(x+2)y = ex b. Solve the Bernoulli’s Equation x2y'−3y2 +2xy = 0, y(2) =5 c. Solve by undetermined coefficients y"− y = x+sinx, y(0)= 2,y'(0) =3

6) Solve the ff IPV: U(X,0) =f(X) b1) 2Ut + (X+1)2UX = 0 b2) Ut +...

6) Solve the ff IPV: U(X,0) =f(X) b1) 2Ut + (X+1)2UX = 0 b2) Ut + Xt^2UX=0 b3) Ut + U^2UX=0

What is the order and type of the ff PDE's. 1. (1+X^2)Uxxyy-2xy^3Uxyyy+(1+u^2)UYY=0 2.(1+U^2)Uxx-2U^2Uxy+(1+u^2)UYY=0 3.(1+X^2Y)Uxx-2UXUyUxy+(1+u^2X)UYY=0

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1,...

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1, t > 0, u(0,t) = 0 = u(1,t), u(x,0) = x/2

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1,...

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1, t > 0, ux(0,t) = 0 = ux(1,t), u(x,0) = 1 - x2

Solve the following initial value problems: a) ut+xux= -tu, x is in R, t>0; u(x,0) =f(x),...

Solve the following initial value problems: a) ut+xux= -tu, x is in R, t>0; u(x,0) =f(x), x is in R. c) ut+ux=-tu, x is in R, t>0; u(x,0)=f(x), x is in R d)2ut+ux = -2u, x,t in R, t>0; u(x,t)=f(x,t) on the straight line x = t, where f is a given function.

Consider the equation utt = uxx x ∈ (0, pi) ux(0,t) = u(pi,t) = 0 Write...

Consider the equation utt = uxx x ∈ (0, pi) ux(0,t) = u(pi,t) = 0 Write the series expansion for a solution u(x,t)

Solve the Boundary Value Problem, PDE: Utt-a2uxx=0, 0≤x≤1, 0≤t<∞ BCs: u(0,t)=0 u(1,t)=cos(t) u(x,0)=0 ut(x,0)=0

Solve the following IVP specifically using the Laplace transform method (d^3)x/d(t^3)+x=e^(-t)u(t) f(0)=0 f'(0)=0 f''(0)=0...

Solve the following IVP specifically using the Laplace transform method (d^3)x/d(t^3)+x=e^(-t)u(t) f(0)=0 f'(0)=0 f''(0)=0 where u(t) is the Heaviside step function

Question

Use separation of variables to solve uxx+2uy+uyy=0, u(x, 0) = f(x), u(x, 1) = 0, u(0,...

Solutions

Expert Solution

Related Solutions

Please solve the following: ut=uxx, 0<x<1, t>0 u(0,t)=0, u(1,t)=A, t>0 u(x,0)=cosx, 0<x<1

1. Solve by separation of variables yy'= xy2 + x, y(1)=0 a. Solve by the integrating...

6) Solve the ff IPV: U(X,0) =f(X) b1) 2Ut + (X+1)2UX = 0 b2) Ut +...

What is the order and type of the ff PDE's. 1. (1+X^2)Uxxyy-2xy^3Uxyyy+(1+u^2)UYY=0 2.(1+U^2)Uxx-2U^2Uxy+(1+u^2)UYY=0 3.(1+X^2Y)Uxx-2UXUyUxy+(1+u^2X)UYY=0

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1,...

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1,...

Solve the following initial value problems: a) ut+xux= -tu, x is in R, t>0; u(x,0) =f(x),...

Consider the equation utt = uxx x ∈ (0, pi) ux(0,t) = u(pi,t) = 0 Write...

Solve the Boundary Value Problem, PDE: Utt-a2uxx=0, 0≤x≤1, 0≤t<∞ BCs: u(0,t)=0 u(1,t)=cos(t) u(x,0)=0 ut(x,0)=0

Solve the following IVP specifically using the Laplace transform method (d^3)x/d(t^3)+x=e^(-t)u(t) f(0)=0 f'(0)=0 f''(0)=0...